Such a delivery device is known, for example, from DE 20 2004 015 442 U1. A drive motor configured as an electric motor is used in this prior-art delivery device to drive two delivery wheels of a fuel-operated vehicle heater. A first of these delivery wheels is used to deliver combustion air as a gaseous first medium into a burner area of the vehicle heater. A second of these delivery wheels is used to deliver heating air as a gaseous second medium in the direction of a heat exchanger unit of the vehicle heater.